A simple apparatus and special techniques are described which have been used to purify and to grow single crystals of KCl and KBr. The measured inpurity content of such crystals is lower than that of commonly used, commercially available crystals by a large factor. Residual impurities have fractional concentrations, in most cases, of less than ten parts per billion. The techniques used, with appropriate modifications, can be employed for the growth of most of the other alkali halides.